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Solution - Why is the Weight of an Object on the Moon 1/6th Its Weight on the Earth? - CBSE Class 9 - Science

ConceptMass and Weight

Question

Why is the weight of an object on the moon 1/6th its weight on the earth?

Solution

Let ME be the mass of the Earth and m be an object on the surface of the Earth. Let RE be the radius of the Earth. According to the universal law of gravitation, weight WE of the object on the surface of the Earth is given by,

`W_E=(GM_Em)/R_E^2`

Let MM and Rbe the mass and radius of the moon. Then, according to the universal law of gravitation, weight WM of the object on the surface of the moon is given by:-

`W_E=(GM_Mm)/R_M^2`

`W_M/W_E=(M_MR_E^2)/(M_ER_M^2)`

`"Where, "M_E=5.98xx10^24kg," "M_M=7.36xx10^22kg`

`R_E=6.4xx10^6m," "R_M=1.74xx10^6m`

`thereforeW_M/W_E=(7.36xx10^22xx(6.37xx10^6)^2)/(5.98xx10^24xx(1.74xx10^6)^2)=0.165approx1/6`

Therefore, weight of an object on the moon is `1/6` of its weight on the Earth.

Is there an error in this question or solution?

APPEARS IN

 NCERT Science Textbook for Class 9 (with solutions)
Chapter 10: Gravitation
Q: 2 | Page no. 138

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Reference Material

Solution for question: Why is the Weight of an Object on the Moon 1/6th Its Weight on the Earth? concept: null - Mass and Weight. For the course CBSE
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